"From clonal interference to Poissonian interacting trajectories"Wakolbinger, AntonWe consider a population whose size is fixed over the generations, and in which beneficial mutations arrive at a small rate. In an essentially homogeneous background the early phase of such a mutant family is governed by a branching process. We focus on the so-called Gerrish-Lenski regime, in which typically a finite number of contending mutations is present together with one resident type. These mutations compete for fixation, a phenomenon addressed as clonal interference. We show that for large population size the rescaled logarithmic sizes of the contending mutant families constitute a system of interacting piecewise linear trajectories driven by a Poisson point process, and relate the speed of adaptation in this system to heuristic predictions from the literature. Our analysis will be carried out for a continuous-time Moran model and for strong selection with random fitness increments. We conjecture that our results extend to a wide range of reproduction dynamics as well as to moderate selection. The talk is based on joint work in progress with Felix Hermann, Adrián González Casanova, Renato Soares dos Santos, and András Tobiás. |
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